Geology Reference
In-Depth Information
and meters for dry snow. More data on penetration depth
of microwave frequencies are presented in section 8.5.
Penetration depth in the snow is important for interpreta-
tion of observations from snow‐covered sea ice. Snow on
sea ice usually becomes stratified as the snow ages and is
exposed to different weather conditions. The contribution
of snow to the observed signal is different from different
layers, but in general the microwave emission tends to
decrease almost exponentially with the snow depth
[
Parkinson et al.,
1987].
such as freshwater ice or MY ice ″ can be much smaller
than the real part ′, then
j
2
(7.34)
Substituting equation (7.34) into (7.33) yields
)
(7.35)
kz
(
jkz
EEe
e
2
0
7.4. oPtical sensinG
The exponents in the above equation define the attenua-
tion (absorption) constant
α
and the phase constants
β
:
As mentioned before, optical remote sensing refers to
the measuring of the reflection of the solar radiation in
the visible and NIR bands (Figure 7.1). In general, the
Earth's surface reflects roughly 37% of the solar radia-
tion impinging on it, though most of the reflected radia-
tion is in the visible band. Measurements from optical
sensors are presented in the form of reflectance at the top
of the atmosphere (TOA). Surface reflectance can be
retrieved from the TOA observations after accounting for
atmospheric effects that include absorption, scattering,
and emission of radiation. Reflectance depends on the
geometry of the incident radiation and the viewing angle
of the sensor; therefore, it is a directional function. A
standard reference of reflectance nomenclature is pre-
sented in
Nicodemus et al.
[1977]. Reflectance is measured
in terms of the bidirectional reflectance distribution
function (BRDF) and the albedo. The former has limited
use in sea ice, but it is introduced in the following to clar-
ify the notion of the albedo.
The irradiance received at any point on Earth's surface
is almost always reflected in many directions. An idealiza-
tion of this directional behavior is represented by the
equal reflection pattern in all directions (isotropic scat-
tering). Figure 7.20 illustrates the difference between
isotropic and anisotropic scattering. The surface that
exhibits an isotropic scattering pattern is called a
Lambertian surface. In nature, the rougher the surface
the closer its behavior would be to Lambertian scattering,
but the reverse is not true. Sea ice surface can be distinctly
considered as non‐Lambertian. This is mainly because
the combined effects of the ice-snow surface makes the
surface nonuniformly rough with respect to the short
wavelengths of the solar irradiance.
In the case of a non‐Lambertian surface the measured
reflection depends on the directions of both the incident
radiation and scattering pattern. That leads to the use
of the term “bidirectional reflectance.” The BRDF
gives the ratio of the reflectance of a surface in a certain
direction to the would‐be uniform (isotropic) reflec-
tance of the same radiation from a Lambertian surface.
It is a frequency‐dependent function that describes the
k
(7.36)
2
and
k
(7.37)
In the case of a generally lossy medium, which is the case
of saline FY ice, equation (7.34) can be written as
)
/
12
(7.38)
(
1
j
tan
where tan
δ
is called the loss tangent:
(7.39)
tan
It is defined as the tangent of the angle in a plane between
the lossy and the lossless components of an EM field.
Using equations (7.37) and (7.38), the attenuation coeffi-
cient
α
can be redefined as [
Ulaby et al.,
1981, page 225]
12
/
12
/
2
2
1
1
(7.40)
2
where
μ
is the permeability, which is almost equal to
1 in the microwave region for most material. The pene-
tration depth is defined as half of the attenuation
coefficient:
1
2
(7.41)
p
This is another form of equation (3.70). At the 1.55 cm
wavelength (near the operational passive microwave fre-
quency of 18 GHz), the penetration depth is on the order
of millimeters for OW and FY ice, decimeters for MY ice,
